An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s(t) is the distance dropped after t seconds, then the speed is v = s'(t) and the acceleration is a = v'(t). If g is the acceleration due to gravity, then the downward force on the object is mg − cv, where c is a positive constant, and Newton's Second Law givesmdvdt = mg − cv.(a) Solve this as a linear equation. (Use v for v(t).)v=mgC(1−e−(Cm)t) (b) What is the limiting velocity?lim t → ∞ v(t) = mgc (c) Find the distance the object has fallen after t seconds. (Use s for s(t).) An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s(t) is the distance dropped after t seconds, then the speed is v = s'(t) and the acceleration is a = v'(t). Ifg is the acceleration due to gravity, then the downward force on the object is mg - cv, where c is a positive constant, and Newton's Second Law givesmdv = mg - cv.(a) Solve this as a linear equation. (Use v for v(t).)(b) What is the limiting velocity?lim v(t) =mg(c) Find the distance the object has fallen after t seconds. (Use s for s(t).)mgtle

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An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s(t) is the distance dropped after t seconds, then the speed is v = s'(t) and the acceleration is a = v'(t). If g is the acceleration due to gravity, then the downward force on the object is mg - cv, where c is a positive constant, and Newton's Second Law gives mdv = mg - cv. (a) Solve this as a linear equation. (Use v for v(t).) (b) What is the limiting velocity? lim v(t) = mg (c) Find the distance the object has fallen after t seconds. (Use s for s(t).) mgt le

An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s(t) is the distance dropped after t seconds, then the speed is v = s'(t) and the acceleration is a = v'(t). If g is the acceleration due to gravity, then the downward force on the object is mg - cv, where c is a positive constant, and Newton's Second Law gives mdv = mg - cv. (a) Solve this as a linear equation. (Use v for v(t).) (b) What is the limiting velocity? lim v(t) = mg (c) Find the distance the object has fallen after t seconds. (Use s for s(t).) mgt le

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter6: Motion In Two Dimensions

Section6.3: Relative Velocity

Problem 27PP

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An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If

s(t)

is the distance dropped after t seconds, then the speed is

v = s'(t)

and the acceleration is

a = v'(t).

If g is the acceleration due to gravity, then the downward force on the object is

mg − cv,

where c is a positive constant, and Newton's Second Law gives

= mg − cv.

(a) Solve this as a linear equation. (Use v for v(t).)

v=mgC(1−e−(Cm)t)

(b) What is the limiting velocity?

lim t → ∞ v(t) =

mgc

An object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s(t) is the distance dropped after t seconds, then the speed is v = s'(t) and the acceleration is a = v'(t). If
g is the acceleration due to gravity, then the downward force on the object is mg - cv, where c is a positive constant, and Newton's Second Law gives
mdv = mg - cv.
(a) Solve this as a linear equation. (Use v for v(t).)
(b) What is the limiting velocity?
lim v(t) =
mg
(c) Find the distance the object has fallen after t seconds. (Use s for s(t).)
mgt
le

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